Cook broccoli in a large pot of boiling salted water until crisp-tender, about 4 minute Using a slotted spoon remove broccoli to a large bowl. Add fusilli to same pot and cook pasta al dente (almost done). Drain pasta.
Meanwhile, heat oil in a heavy large skillet over high heat. Crush garlic and add to oil, slice chicken to 1/2 inch strips and add to oil. Be careful not to let the garlic brown or burn. Cook chicken about 5 minutes.
Using slotted spoon, transfer chicken to a bowl with broccoli. Add wine, chicken broth and cream to the skillet and boil until sauce thickens slightly, about 8 minute Add pasta, broccoli, chicken, and parmesan and toss until mixture is heated through and coated evenly with sauce.